The Least Squares Solutions of Inverse Problems of Unified Algebraic Lyapunov Equation

Bounds for solutions of the discrete algebraic Lyapunov equation

A family of sharp, arbitrarily tight, upper and lower matrix bounds for solutions of the discrete algebraic Lyapunov are presented. The lower bounds are tighter than previously known ones. Unlike the majority of previously known upper bounds, those derived here have no restrictions on their applicability. Upper and lower bounds for individual eigenvalues and for the trace of the solution are fo...

On the Least Squares Solution of Inverse Eigenvalue Problems

An inverse eigenvalue problem where a matrix is to be constructed from some or all of its eigenvalues may not have a real valued solution at all An approximate solution in the sense of least squares is sometimes desirable Two types of least squares problems are formulated and explored in this paper In spite of their di erent appearance the two problems are shown to be equivalent Thus one new nu...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion

The aim of physical sciences is to discover the minimal set of parameters which completely describe physical systems and the laws relating the values of these parameters to the results of any set of measurements on the system. A coherent set of such laws is named a physical theory. To the extent that the values of the parameters can only be obtained as a results of measurements, one may equival...

Fast Enclosure for Solutions of Generalized Least Squares Problems∗

Fast algorithms for enclosing solutions of generalized least squares problems are proposed. To develop these algorithms, theories for obtaining error bounds on numerical solutions are established. The error bounds obtained by these algorithms are “verified” in the sense that all the possible rounding errors have been taken into account. A technique for obtaining smaller error bounds is introduc...